Random line graphs and edge-attributed network inference

We extend the latent position random graph model to the line graph of a random graph, which is formed by creating a vertex for each edge in the original random graph, and connecting each pair of edges incident to a common vertex in the original graph. We prove concentration inequalities for the spectrum of a line graph, as well as limiting distribution results for the largest eigenvalue and the empirical spectral distribution in certain settings. For the stochastic blockmodel, we establish that although naive spectral decompositions can fail to extract necessary signal for edge clustering, there exist signal-preserving singular subspaces of the line graph that can be recovered through a carefully-chosen projection. Moreover, we can consistently estimate edge latent positions in a random line graph, even though such graphs are of a random size, typically have high rank, and possess no spectral gap. Our results demonstrate that the line graph of a stochastic block model exhibits underlying block structure, and in simulations, we synthesize and test our methods against several commonly-used techniques, including tensor decompositions, for cluster recovery and edge covariate inference. By naturally incorporating information encoded in both vertices and edges, the random line graph improves network inference.Comment: 44 pages total, including supplementary material; 5 figure

Discovering underlying dynamics in time series of networks

Understanding dramatic changes in the evolution of networks is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We consider a joint network model in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the time-varying evolution of the constellation of latent vectors exhibits low-dimensional manifold structure under a suitable notion of distance. This distance can be approximated by a measure of separation between the observed networks themselves, and there exist consistent Euclidean representations for underlying network structure, as characterized by this distance, at any given time. These Euclidean representations permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. We illustrate our methodology with real and synthetic data, and identify change points corresponding to massive shifts in pandemic policies in a communication network of a large organization.Comment: 31 pages, 7 figure

Animal Models of Bone Loss in Inflammatory Arthritis: from Cytokines in the Bench to Novel Treatments for Bone Loss in the Bedside—a Comprehensive Review

Throughout life, bone is continuously remodelled. Bone is formed by osteoblasts, from mesenchymal origin, while osteoclasts induce bone resorption. This process is tightly regulated. During inflammation, several growth factors and cytokines are increased inducing osteoclast differentiation and activation, and chronic inflammation is a condition that initiates systemic bone loss. Rheumatoid arthritis (RA) is a chronic inflammatory auto-immune disease that is characterised by active synovitis and is associated with early peri-articular bone loss. Peri-articular bone loss precedes focal bone erosions, which may progress to bone destruction and disability. The incidence of generalised osteoporosis is associated with the severity of arthritis in RA and increased osteoporotic vertebral and hip fracture risk. In this review, we will give an overview of different animal models of inflammatory arthritis related to RA with focus on bone erosion and involvement of pro-inflammatory cytokines. In addition, a humanised endochondral ossification model will be discussed, which can be used in a translational approach to answer osteoimmunological questions